Marton's inner bound is the best known achievable region for a general
discrete memoryless broadcast channel. To compute Marton's inner bound one has
to solve an optimization problem over a set of joint distributions on the input
and auxiliary random variables. The optimizers turn out to be structured in
many cases. Finding properties of optimizers not only results in efficient
evaluation of the region, but it may also help one to prove factorization of
Marton's inner bound (and thus its optimality).
P2P systems provide a scalable solution for distributing large files in a
network. The file is split into many chunks, and peers contact other peers to
collect missing chunks to eventually complete the entire file. The so-called
`rare chunk' phenomenon, where a single chunk becomes rare and prevents peers
from completing the file, is a threat to the stability of such systems.
Practical systems such as BitTorrent overcome this issue by requiring a global
search for the rare chunk, which necessitates a centralized mechanism.